After starting a process from third party application by hitting the service of

You can create a WebAPI to query tasks by the process id returned by the web service call.

how do we do that? I have created a webAPI. How to Query task? Does querying task give us a task id or task link?

Check forum.appian.com/.../Process_Reports.html. Then you use queryprocessanalytics() to query this report. It returns the data in any format you like, including the task id.

is it necessary to create a report? I am interested in making a WebAPI which takes in processId and returns taskId.

Yes. A process report, or portal report in pre 7.11, lets you gather data from the process executions engines. A process report is different from a tempo report. It acts as a datasource similar to a database when using queryentity().

There is a custom function getActiveTaskIDsForProcess(), you can use it in your WebAPI. Here is the link to the custom function,
forum.appian.com/.../summary

This has already been answered in your previous question: forum.appian.com/.../e-187492

philb, I still am not able to do it, that's why I asked the question. I want more insight to the response which I got

Ok - to join everything together on this question and expand on the previous one, you'll need to create a process report that runs in the context of the process model that is being started and shows the task ID within that process, then create a Web API that accepts a process ID and uses a!queryProcessAnalytics() to obtain and return the task ID from the aforementioned report.

The documentation you'll need is linked below; you may also want to look at the task report tutorial if you're struggling with a!queryProcessAnalytics().

Process reports: forum.appian.com/.../Process_Reports.html
Web APIs: forum.appian.com/.../Web_API_Tutorial.html
a!queryProcessAnalytics: forum.appian.com/.../System_Functions.html
Task report tutorial: forum.appian.com/.../Task_Report_Tutorial.html

How to show taskId? Do I need to add new data in the process report?